Finding components of final velocity- on homework

[timemachinez]

The problem states that a plane approaching a mountain peak at a speed of 50 m/s is located at a vertical distance of 100.0 m above the peak.

I calculated the distance at which the plane should release the package so it lands on the peak (first question), but the second question ask what the vertical component of the package's velocity is before it lands on the peak.

the third question asks for the magnitude and direction of the final velocity before it lands on the peak

I'm not even sure how to approach this.

 

[The Bob]

Welcome to PF timemachinez!

Do you understand what the vertical component is (as you've enboldened it)? If you know the distance at which it was released then you can form angles between velocity vectors. Are we neglecting air resistance and gravity?

The Bob

 

[timemachinez]

well, I think it's including gravity, but not air resistance. I figured that if I had the distance, I could find the angles, but I'm not sure if I'm either brain dead or can't visualize how to do this.

 

[timemachinez]

I just calculated the angle by using arctan ...and I think I might get what I need to do! haha

 

[timemachinez]

I take that back. I found the net distance by using the pythagorean theorem, and found the angles of the triangle, but I don't know if that's what I even need.

 

[The Bob]

Yes, the vertical component in this case is gravity, assuming the plan is flying horizontally, but it is not a constant velocity vector but a constant acceleration vector (something around 9.8ms^-2). So what you need to do is find out how long it will take the package to fall 100m from rest and then, from this, you can work out the distance from the peak at which the package was released. Helping?

The Bob

 

[timemachinez]

I used basic formulas to find the component of the velocity and then later on the magnitude and direction (that was the 3rd question).

I just need to make sure that the time I got was right, because otherwise it throws everything off.
I used x=x₀+v₀t+.5at²

since there's no velocity when an object is falling, I plugged in zero for that and got that
100=0+4.9t² finally giving me 4.52 seconds. I plugged that into the horizontal component which I said was x=0+50t (for the formula v_f=v_I+at

I then got that the package should be dropped 226 m away. Since its traveling 4.52 seconds, I multiplied that by 9.8 to get the vertical component of the velocity.

I think that's correct?

 

[The Bob]

Hey,

Rounding to 3 significant figures each time, your workings and thinking are right. So next question: What is the vertical component of the package's velocity before it lands on the peak? Think about what is happening in the vertical direction and pick an equation you're already mentioned. Try using words first if it helps.

The Bob